Cyclic Hilbert Spaces and Connes’ Embedding Problem

Connes ’ embedding problem and Tsirelson ’ s problem

We show that Tsirelson’s problem concerning the set of quantum correlations and Connes’ embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg’s QWEP conjecture) are essentially equivalent. Specifically, Tsirelson’s problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the...

Computability and the Connes Embedding Problem

The Connes Embedding Problem (CEP) asks whether every separable II1 factor embeds into an ultrapower of the hyperfinite II1 factor. We show that the CEP is equivalent to the statement that every type II1 tracial von Neumann algebra has a computable universal theory.

Connes’ Embedding Problem and Lance’s Wep

A II1-factor embeds into the ultraproduct of the hyperfinite II1-factor if and only if it satisfies the von Neumann algebraic analogue of Lance’s weak expectation property (WEP). This note gives a self contained proof of this fact.

The Coarse Baum – Connes Conjecture for Spaces Which Admit a Uniform Embedding into Hilbert Space

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...